GATE 2016 EC – Question 55
The open-loop transfer function of a unity-feedback control system is
$$G(s) = \frac{K}{s^2 + 5s + 5}$$
The value of $K$ at the breakaway point of the feedback control system's root-locus plot is ________
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1.2 to 1.3
Explanation
The root locus satisfies $K = -(s^2 + 5s + 5)$. A breakaway point is where $\frac{dK}{ds} = 0$, so $-(2s + 5) = 0$ and $s = -2.5$. At that point $K = -(6.25 - 12.5 + 5) = 1.25$.